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<div class="subTitle">org.apache.commons.math3.fitting</div>
<h2 title="Class HarmonicCurveFitter.ParameterGuesser" class="title">Class HarmonicCurveFitter.ParameterGuesser</h2>
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<pre>public static class <span class="strong">HarmonicCurveFitter.ParameterGuesser</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">This class guesses harmonic coefficients from a sample.
 <p>The algorithm used to guess the coefficients is as follows:</p>

 <p>We know \( f(t) \) at some sampling points \( t_i \) and want
 to find \( a \), \( \omega \) and \( \phi \) such that
 \( f(t) = a \cos (\omega t + \phi) \).
 </p>

 <p>From the analytical expression, we can compute two primitives :
 \[
     If2(t) = \int f^2 dt  = a^2 (t + S(t)) / 2
 \]
 \[
     If'2(t) = \int f'^2 dt = a^2 \omega^2 (t - S(t)) / 2
 \]
 where \(S(t) = \frac{\sin(2 (\omega t + \phi))}{2\omega}\)
 </p>

 <p>We can remove \(S\) between these expressions :
 \[
     If'2(t) = a^2 \omega^2 t - \omega^2 If2(t)
 \]
 </p>

 <p>The preceding expression shows that \(If'2 (t)\) is a linear
 combination of both \(t\) and \(If2(t)\):
 \[
   If'2(t) = A t + B If2(t)
 \]
 </p>

 <p>From the primitive, we can deduce the same form for definite
 integrals between \(t_1\) and \(t_i\) for each \(t_i\) :
 \[
   If2(t_i) - If2(t_1) = A (t_i - t_1) + B (If2 (t_i) - If2(t_1))
 \]
 </p>

 <p>We can find the coefficients \(A\) and \(B\) that best fit the sample
 to this linear expression by computing the definite integrals for
 each sample points.
 </p>

 <p>For a bilinear expression \(z(x_i, y_i) = A x_i + B y_i\), the
 coefficients \(A\) and \(B\) that minimize a least-squares criterion
 \(\sum (z_i - z(x_i, y_i))^2\) are given by these expressions:</p>
 \[
   A = \frac{\sum y_i y_i \sum x_i z_i - \sum x_i y_i \sum y_i z_i}
            {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i}
 \]
 \[
   B = \frac{\sum x_i x_i \sum y_i z_i - \sum x_i y_i \sum x_i z_i}
            {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i}

 \]

 <p>In fact, we can assume that both \(a\) and \(\omega\) are positive and
 compute them directly, knowing that \(A = a^2 \omega^2\) and that
 \(B = -\omega^2\). The complete algorithm is therefore:</p>

 For each \(t_i\) from \(t_1\) to \(t_{n-1}\), compute:
 \[ f(t_i) \]
 \[ f'(t_i) = \frac{f (t_{i+1}) - f(t_{i-1})}{t_{i+1} - t_{i-1}} \]
 \[ x_i = t_i  - t_1 \]
 \[ y_i = \int_{t_1}^{t_i} f^2(t) dt \]
 \[ z_i = \int_{t_1}^{t_i} f'^2(t) dt \]
 and update the sums:
 \[ \sum x_i x_i, \sum y_i y_i, \sum x_i y_i, \sum x_i z_i, \sum y_i z_i \]

 Then:
 \[
  a = \sqrt{\frac{\sum y_i y_i  \sum x_i z_i - \sum x_i y_i \sum y_i z_i }
                 {\sum x_i y_i  \sum x_i z_i - \sum x_i x_i \sum y_i z_i }}
 \]
 \[
  \omega = \sqrt{\frac{\sum x_i y_i \sum x_i z_i - \sum x_i x_i \sum y_i z_i}
                      {\sum x_i x_i \sum y_i y_i - \sum x_i y_i \sum x_i y_i}}
 \]

 <p>Once we know \(\omega\) we can compute:
 \[
    fc = \omega f(t) \cos(\omega t) - f'(t) \sin(\omega t)
 \]
 \[
    fs = \omega f(t) \sin(\omega t) + f'(t) \cos(\omega t)
 \]
 </p>

 <p>It appears that \(fc = a \omega \cos(\phi)\) and
 \(fs = -a \omega \sin(\phi)\), so we can use these
 expressions to compute \(\phi\). The best estimate over the sample is
 given by averaging these expressions.
 </p>

 <p>Since integrals and means are involved in the preceding
 estimations, these operations run in \(O(n)\) time, where \(n\) is the
 number of measurements.</p></div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html#HarmonicCurveFitter.ParameterGuesser(java.util.Collection)">HarmonicCurveFitter.ParameterGuesser</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../org/apache/commons/math3/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.fitting">WeightedObservedPoint</a>&gt;&nbsp;observations)</code>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/fitting/HarmonicCurveFitter.ParameterGuesser.html#guess()">guess</a></strong>()</code>
<div class="block">Gets an estimation of the parameters.</div>
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<h4>HarmonicCurveFitter.ParameterGuesser</h4>
<pre>public&nbsp;HarmonicCurveFitter.ParameterGuesser(<a href="http://docs.oracle.com/javase/6/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../org/apache/commons/math3/fitting/WeightedObservedPoint.html" title="class in org.apache.commons.math3.fitting">WeightedObservedPoint</a>&gt;&nbsp;observations)</pre>
<div class="block">Simple constructor.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>observations</code> - Sampled observations.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the sample is too short.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if the abscissa range is zero.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</a></code> - when the guessing procedure cannot
 produce sensible results.</dd></dl>
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<h4>guess</h4>
<pre>public&nbsp;double[]&nbsp;guess()</pre>
<div class="block">Gets an estimation of the parameters.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the guessed parameters, in the following order:
 <ul>
  <li>Amplitude</li>
  <li>Angular frequency</li>
  <li>Phase</li>
 </ul></dd></dl>
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